By removing edges not involved in some solution,
and contracting edges involved in all solutions,
we reduce the problem to one in a graph with O(k)
edges and vertices. This simplification step
transforms any time bound involving m or n
to one involving min(m,k) or min(n,k)
respectively. This paper also introduces the geometric
version of the k smallest spanning trees problem
(the graph version was long known) which it solves using
order (k+1) Voronoi diagrams.